Roy Hodgson's grip on his position as Liverpool manager appears to be
loosening after comments suggesting he had never enjoyed the full support of
the fans prompted a furious backlash on Merseyside.

His remarks, made in the aftermath of the 1-0 defeat to bottom club Wolves, are also believed to have caused concern among the club's hierarchy, who fear his relationship with the Anfield public may now be stretched beyond repair.

Hodgson stated after the defeat to Mick McCarthy's side on Wednesday that he hoped Liverpool's "fans would become supporters" after failing to offer him their backing throughout his six-month reign.

The comments were seen as a serious error of judgment by the club's owners, Fenway Sports Group. Thousands of fans demanded his dismissal on websites and internet polls, with one survey finding that 97 per cent of supporters favoured his departure.

Though John W Henry and Tom Werner, the American group's principal backers, have shown nothing but support in public for their beleaguered manager, in private they are believed to harbour concerns that the furore marks the end of any hope he had of winning over the fans, who offered ironic chants of "Hodgson for England".

FSG had hoped to allow Hodgson to continue until the summer – when his position would be reviewed – but concerns are growing that, should results continue to prompt almost unprecedented insurrection in Anfield's stands, they may need to act much more quickly.

Liverpool face Bolton at Anfield on Saturday before travelling to Blackburn on Wednesday. That is followed by an FA Cup fixture against Manchester United. A programme of five games in 15 days is rounded off by a Premier League fixture with Blackpool, rearranged from Boxing Day, and the Merseyside derby with Everton.

There remains little appetite for a change of manager mid-season – especially with such an intimidating schedule looming – but with the club hovering just three points above the relegation zone, FSG know poor results might force their hand.

The sound of Anfield voicing its displeasure will not, at least, have come as a surprise. Henry and Werner are well aware that Kenny Dalglish's name has been chanted several times this season, while the pair's appearance on a phone-in on the club's official television channel this month triggered a string of calls demanding Hodgson's dismissal.

Then, Werner and Henry offered Hodgson time to rectify the early errors of his reign. Werner admitted that "performance has to improve, especially on the road, but we believe in what he is doing", but made clear the pair's displeasure at Liverpool's poor league performance. "This season and the last half of last season were unacceptable for Liverpool," said Henry. "We are in sync with fans for what it is going to take."

Given the nature of Liverpool's capitulation against Wolves – the visiting goalkeeper, Wayne Hennessey, did not make a save of note in the second half – FSG are unlikely to believe that Hodgson is the man to entrust with that task. It is thought both Henry and Werner are concerned that the former Fulham manager may not retain the faith of the club's squad, despite his statements to the contrary.

The fans, too, made it clear on Wednesday that they would like Dalglish installed immediately, at least until the end of the season. FSG, though, are not thought to favour appointing an interim manager, should they dispense with Hodgson. The group wish to rebuild the club around a young coach.

While such a policy almost certainly condemns Hodgson at the end of the season, it may help secure his position in the short term. Of those managers who FSG could identify to take charge for the coming seasons, only Frank Rijkaard, the former Barcelona coach, is not under contract.

Hodgson is unlikely to be the only victim of Liverpool's season of nadirs. Liverpool will announce the departure of chief scout Eduardo Macia by mutual consent on Friday, and with the club's wage bill running at more than £100 million a year, FSG are thought to be increasingly convinced of the need for a major overhaul of the playing staff in the summer.

The Liverpool manager has made it clear he does not wish to sell any players in January – his dismissal of suggestions from Wolfsburg that they had been offered the chance to sign Daniel Agger, and the imminent recruitment of Sylvain Marveaux from Rennes, suggests the emphasis is on strengthening resources – but either he or his replacement may have to oversee an exodus in June.

Few who played on Wednesday improved their chances of remaining at Anfield beyond this season, with Ryan Babel admitting on his Twitter account that he did not have the "words to describe" the performance, while admonishing the club's fans for turning on Paul Konchesky. FSG must decide whether it is those players, or Hodgson himself, who is first to depart.